Astrid wants you to speak with Amaund Motierre at Volunruud. Head inside this dungeon to find a brown leather-bound journal sitting right at the entrance. Inspecting this begins Silenced Tongues, which can be done simultaneously with this quest.

Amaund is waiting in a room off to the side with his servant, Rexus. You receive a valuable amulet and a sealed letter. Read or don’t read the letter yourself -- you will soon learn what the assassination contract is for.

Deliver letter and amulet to Astrid. Astrid wants you to show the amulet to Devin Mallory in Riften, in a bar called The Ragged Flagon (the hideout for the Thieves' Guild) within an underground area called The Ratway. After showing Mallory the amulet, he will take it and give you a Letter of Credit. Take this letter back to Astrid.